On the Fourier coefficients of linear fractional stable motion

Inspired by a theorem of Marcinkiewicz J. Marcinkiewicz, On a class of functions and their Fourier series, C. R. Soc. Sci. Varsovie, 26:71–77, 1934. Reprinted in: J. Marcinkiewicz, Collected Papers (A. Zygmund (Ed.)), PaństwoweWydawnictwo Naukowe,Warsaw, 1964] stating that the maximum of the absolute values of real Fourier coefficients a _n and b _n of a function of bounded p-variation ( p \geqslant 1 ) \left( {p \geqslant 1} \right) on an interval 0, 1] is of order O(n ^−1/p ) as n → ∞, we compute the Fourier coefficients of the linear fractional stable motion (LFSM) and of the closely related Riemann–Liouville (RL) process and investigate the rate of their decay.